Problem $7-(20$ Points$)$: $(10$ pts each$)$

In the noninverting amplifier shown below, resistor $R_2$ deviates from its nominal value by $R.$

Assume the op$-$amp has finite openloop gain $A{l}_0$

$($a$)$ First, derive the nominal voltage gain expression of $\frac{v_{\text{o}\text{u}\text{t}}}{v_{in}},$ then

$($b$)$ calculate the gain error of the circuit if $\frac{R}{R_2}1.$